A114795 {concatenation n, n-1, n-2, ...3,2,1} mod n.

0, 1, 0, 1, 1, 3, 3, 1, 0, 1, 6, 9, 2, 1, 6, 1, 4, 9, 0, 1, 12, 17, 4, 9, 21, 21, 0, 13, 11, 21, 20, 17, 6, 29, 1, 9, 8, 25, 36, 1, 0, 33, 41, 17, 36, 23, 26, 33, 34, 21, 30, 41, 38, 27, 6, 1, 36, 39, 7, 21, 31, 59, 54, 49, 21, 39, 57, 45, 60, 41, 31, 9, 37, 41, 21

Offset: 1

Author

Amarnath Murthy, Nov 19 2005

Keywords

• base
• nonn

Examples

			a(7) = 7654321 mod 7 = 3.
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000422.

Programs

Mathematica

f[n_] := Mod[FromDigits@ Flatten@ IntegerDigits@ Reverse@ Range@ n,
n]; Array[f, 75] (* or *)
f[n_] := Fold[Mod[#1*10^Floor[1 + Log10@#2] + #2, n] &, 0,
  Reverse@Range@n]; Array[f, 75] (* Robert G. Wilson v, Jan 10 2017 *)

Python

def A114795(n):
    s=""
    for i in range(n,0,-1):
        s+=str(i)
    return int(s)%n # Indranil Ghosh, Jan 10 2017

Formula

a(n) = A000422(n) mod n. - Michel Marcus, Jan 10 2017

Extensions

More terms from Ryan Murphy (murphy(AT)minegoboom.com) and Evonne Haines (avissean(AT)adelphia.net), Jan 21 2006